Related papers: A Categorical Model for Classical and Quantum Bloc…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
The block-oriented models are usually based on linear dynamic and non-linear static blocks that are connected in various sequential/parallel ways. Some particular configurations of the involved blocks result in the well-known Hammerstein,…
The field of quantum computing is at an exciting time where we are constructing novel hardware, evaluating algorithms, and finding out what works best. As qubit technology grows and matures, we need to be ready to design and program larger…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing…
Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of…
In this work, we present a complete hybrid classical-quantum algorithm involving a quantum sampler based on neutral atom platforms. This approach is inspired by classical column generation frameworks developed in the field of Operations…
Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…
Constellations are partial algebras that are one-sided generalisations of categories. It has previously been shown that the category of inductive constellations is isomorphic to the category of left restriction semigroups. Here we consider…
Quantum computing is a new way of data processing based on the concept of quantum mechanics. Quantum circuit design is a process of converting a quantum gate to a series of basic gates and is divided into two general categories based on the…
A well known class of objects in combinatorial design theory are {group divisible designs}. Here, we introduce the $q$-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces,…
Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck…
We define novel fully combinatorial models of higher categories. Our definitions are based on a connection of higher categories to "directed spaces". Directed spaces are locally modelled on manifold diagrams, which are stratifications of…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
We introduce the CP*-construction on a dagger compact closed category as a generalisation of Selinger's CPM-construction. While the latter takes a dagger compact closed category and forms its category of "abstract matrix algebras" and…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus…